Abstraction-Based Control Under Quantized Observation With Approximate Opacity Using Symbolic Control Barrier Functions

Abstract

The notion of opacity refers to a condition that external observers cannot distinguish between secret and non-secret states, which is important for security of a plant. On the other hand, the authors have recently proposed a “symbolic control barrier function” that enforces forward invariance on the plant with its finite abstracted model. In this letter, we propose symbolic synthesis achieving both desired behaviors and approximated initial-state opacity. First, a symbolic controller that enforces a desired behavior is synthesized without considering the opacity. Next, we eliminate transitions violating a condition on the opacity, which is induced by the symbolic control barrier function. Finally, it is proved that the controlled plant satisfies the opacity if a deadlock-free sub-transition system is obtained. The proposed method is illustrated with a numerical example on tank volume control.